Geodesic
Adaptive wavelet simulation of weakly compressible flow in a channel with a suddenly expanded section
Naoya Okamoto1 ; Margarete Oliveira Domingues2 ; Katsunori Yoshimatsu3 ; Kai Schneider4
1 Center for Computational Science, Nagoya University, Nagoya, 464–8603, Japan
2 Laboratório Associado de Computação e Matemática Aplicada, Coordenadoria dos Laboratórios Associados, Instituto Nacional de Pesquisas Espaciais, Av. dos Astronautas 1758, 12227-010 São José dos Campos, São Paulo, Brazil
3 EcoTopia Science Institute, Nagoya University, Nagoya, 464–8603, Japan
4 M2P2–CNRS & CMI Aix-Marseille Université, 38 rue F. Joliot-Curie, 13451 Marseille Cedex 20, France
ESAIM. Proceedings, Tome 53 (2016), pp. 38-48.

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We present an adaptive multiresolution simulation method for computing weakly compressible flow bounded by solid walls of arbitrary shape, using a finite volume (FV) approach coupled with wavelets for grid adaptation. A volume penalization method is employed to compute the flow in the Cartesian geometry and to impose the boundary conditions. A dynamical adaption strategy to advance both the locally refined grid and the flow in time uses biorthogonal wavelet transforms at each time step. We assess the quality and efficiency of the method for a two-dimensional flow in a periodic channel with a suddenly expanded section. The results are compared with a reference flow obtained by a non-adaptive FV simulation on a uniform grid. It is shown that the adaptive method allows for substantial reduction of CPU time and memory, while preserving the time evolution of the velocity field obtained with the non-adaptive simulation.
DOI : 10.1051/proc/201653003

Naoya Okamoto 1 ; Margarete Oliveira Domingues 2 ; Katsunori Yoshimatsu 3 ; Kai Schneider 4

1 Center for Computational Science, Nagoya University, Nagoya, 464–8603, Japan
2 Laboratório Associado de Computação e Matemática Aplicada, Coordenadoria dos Laboratórios Associados, Instituto Nacional de Pesquisas Espaciais, Av. dos Astronautas 1758, 12227-010 São José dos Campos, São Paulo, Brazil
3 EcoTopia Science Institute, Nagoya University, Nagoya, 464–8603, Japan
4 M2P2–CNRS & CMI Aix-Marseille Université, 38 rue F. Joliot-Curie, 13451 Marseille Cedex 20, France 
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     author = {Naoya Okamoto and Margarete Oliveira Domingues and Katsunori Yoshimatsu and Kai Schneider},
     title = {Adaptive wavelet simulation of weakly compressible flow in a channel with a suddenly expanded section},
     journal = {ESAIM. Proceedings},
     pages = {38--48},
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     year = {2016},
     doi = {10.1051/proc/201653003},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201653003/}
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Naoya Okamoto; Margarete Oliveira Domingues; Katsunori Yoshimatsu; Kai Schneider. Adaptive wavelet simulation of weakly compressible flow in a channel with a suddenly expanded section. ESAIM. Proceedings, Tome 53 (2016), pp. 38-48. doi : 10.1051/proc/201653003. http://geodesic.mathdoc.fr/articles/10.1051/proc/201653003/

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